## A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time (1998)

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Venue: | Theoretical Computer Science |

Citations: | 103 - 9 self |

### BibTeX

@ARTICLE{Bernardo98atutorial,

author = {Marco Bernardo and Roberto Gorrieri},

title = {A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time},

journal = {Theoretical Computer Science},

year = {1998},

volume = {202},

pages = {1--54}

}

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### Abstract

In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of real-world concurrent systems such as nondeterminism, priorities, probabilities and time, with a particular emphasis on performance evaluation. The purpose of this tutorial is to explain the design choices behind the development of EMPA and how the four features above interact, and to show that a reasonable trade off between the expressive power of the calculus and the complexity of its underlying theory has been achieved.

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Citation Context ...simulation equivalence. 1 Introduction Several process algebras have been proposed in the literature in order to model and analyze concurrent systems. Classical process algebras such as CCS [38], CSP =-=[29]-=-, ACP [6] and LOTOS [10] were concerned only with functional aspects of concurrent systems. This means that actions composing algebraic terms were only given a name, and nothing was said about e.g. th... |

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Citation Context ...rig@cs.unibo.it. 1 1 Introduction 1 Introduction Several process algebras have been proposed in the literature in order to model and analyze concurrent systems. Classical process algebras such as CCS =-=[26]-=-, CSP [20], ACP [4] and LOTOS [9] were concerned only with functional aspects of concurrent systems. This means that actions composing algebraic terms were only given a name, and nothing was said abou... |

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Citation Context ...and to minimize the integrated semantic model of an EMPA term. 5.1 A deceptively integrated equivalence: FP A generally accepted notion of equivalence in the field of process algebras is bisimilarity =-=[30, 26]-=-. Using this approach, it is straightforward to define two projected equivalences based on the two projected semantic models. For the functional semantic model we use classical bisimilarity, whereas f... |

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Citation Context ... has finitely many states, and is unique. Proof See [8]. We conclude by observing that the coexistence in EMPA of the probabilistic and the exponentially timed kernels allows phase-type distributions =-=[40]-=- to be modeled. This makes the limitation to exponential distributions less restrictive, as it becomes possible to describe or approximate distributions frequently occurring in practice. For more deta... |

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Citation Context ...ocess algebras (see e.g. [47, 30, 58, 37, 34, 5, 56]), deterministically timed process algebras (see e.g. [52, 3, 41, 51, 39, 20, 60, 23, 36, 19]), and stochastically timed process algebras (see e.g. =-=[42, 24, 27, 12, 2, 21, 53, 26, 11, 45, 25, 31, 46]-=-). The enhanced expressive power achieved by these classes of process algebras has allowed to model and analyze a greater number of characteristics with respect to classical process algebras such as i... |

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Citation Context ...ove, we exploit the property that the minimum of n independent exponentially distributed random variables is an exponentially distributed random variable whose rate is the sum of the n original rates =-=[22]-=-. As a consequence, for the term above we have that the sojourn time of the corresponding state is exponentially distributed with rate + (hence the mean sojourn time is 1=(+))and the execution probabi... |

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Citation Context ...iate because it is not a congruence. In Section 5.2 we present a notion of equivalence denoted EMB which is defined on the integrated semantic model by refining the idea of probabilistic bisimulation =-=[23]-=- according to the various kernels of EMPA. In Section 5.3 we prove that EMB is a congruence, and in Section 5.4 we demonstrate that EMB is the coarsest congruence contained in FP as far as terms that ... |

428 | Introduction to the ISO specification language LOTOS
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Citation Context ...1 Introduction Several process algebras have been proposed in the literature in order to model and analyze concurrent systems. Classical process algebras such as CCS [38], CSP [29], ACP [6] and LOTOS =-=[10]-=- were concerned only with functional aspects of concurrent systems. This means that actions composing algebraic terms were only given a name, and nothing was said about e.g. their duration. As a conse... |

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Citation Context ...n [43] to solve the relational coarsest partition problem. Given a labeled transition system with state space S representing the union of the integrated semantic models of 4 The reader is referred to =-=[22]-=- for notions and results concerning deductive systems for algebraic theories of concurrent processes. (A 1 ) (E 1 + E 2 ) + E 3 = E 1 + (E 2 + E 3 ) (A 2 ) E 1 + E 2 = E 2 +E 1 (A 3 ) E + 0 = E (A 4 )... |

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Citation Context ... equivalence. 1 Introduction Several process algebras have been proposed in the literature in order to model and analyze concurrent systems. Classical process algebras such as CCS [38], CSP [29], ACP =-=[6]-=- and LOTOS [10] were concerned only with functional aspects of concurrent systems. This means that actions composing algebraic terms were only given a name, and nothing was said about e.g. their durat... |

386 |
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Citation Context ...tion to our framework of the algorithm described in [13] (which could be applied to the functional semantic models of finite-state terms of G), which is in turn a variant of the algorithm proposed in =-=[29]-=- to solve the relational coarsest partition problem. Given a labeled transition system with state space S representing the union of the integrated semantic models of two finite-state terms of G to be ... |

274 | A class of generalized stochastic Petri Nets for the performance evaluation of multiprocessor systems
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Citation Context ...a (EMPA). The development of EMPA has been strongly influenced by the stochastically timed process algebras MTIPP [24] and PEPA [27], and by the formalism of generalized stochastic Petri nets (GSPNs) =-=[1]-=-. This is witnessed by the fact that in EMPA there are three different kinds of actions: exponentially timed actions (taken from MTIPP and PEPA), prioritized weighted immediate actions (analogous to p... |

257 |
Modeling and verification of randomized distributed real-time systems
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- 1995
(Show Context)
Citation Context ... due to the presence of passive actions, thereby causing EMPA pb;l to be viewed as a possible syntactical counterpart of formal models for randomized distributed computations such as those defined in =-=[38]-=-. By performing more accurate comparisons, we see that EMPA pb;l differs from PCCS [21] and WSCCS [40] due to the two reasons above (i.e. introduction of a probabilistic alternative composition operat... |

178 | A temporal calculus of communicating systems - Moller, Tofts - 1990 |

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Citation Context ...resulting in prioritized process algebras (see e.g. [4, 14, 13, 57, 17, 15]), probabilistic process algebras (see e.g. [47, 30, 58, 37, 34, 5, 56]), deterministically timed process algebras (see e.g. =-=[52, 3, 41, 51, 39, 20, 60, 23, 36, 19]-=-), and stochastically timed process algebras (see e.g. [42, 24, 27, 12, 2, 21, 53, 26, 11, 45, 25, 31, 46]). The enhanced expressive power achieved by these classes of process algebras has allowed to ... |

160 | A model for communicating sequential processes
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- 1983
(Show Context)
Citation Context ...resulting in prioritized process algebras (see e.g. [4, 14, 13, 57, 17, 15]), probabilistic process algebras (see e.g. [47, 30, 58, 37, 34, 5, 56]), deterministically timed process algebras (see e.g. =-=[52, 3, 41, 51, 39, 20, 60, 23, 36, 19]-=-), and stochastically timed process algebras (see e.g. [42, 24, 27, 12, 2, 21, 53, 26, 11, 45, 25, 31, 46]). The enhanced expressive power achieved by these classes of process algebras has allowed to ... |

149 | An overview and synthesis of timed process algebras
- Nicollin, Sifakis
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Citation Context ...rations, thereby resulting in prioritized process algebras (see e.g. [2, 11, 12, 39]), probabilistic process algebras (see e.g. [21, 40, 14, 25, 3, 36]), deterministically timed process algebras (see =-=[28, 15]-=- and the references therein), and stochastically timed process algebras (see [31, 32, 33, 34] and the references therein). The enhanced expressive power achieved by these classes of process algebras h... |

115 |
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Citation Context ...resulting in prioritized process algebras (see e.g. [4, 14, 13, 57, 17, 15]), probabilistic process algebras (see e.g. [47, 30, 58, 37, 34, 5, 56]), deterministically timed process algebras (see e.g. =-=[52, 3, 41, 51, 39, 20, 60, 23, 36, 19]-=-), and stochastically timed process algebras (see e.g. [42, 24, 27, 12, 2, 21, 53, 26, 11, 45, 25, 31, 46]). The enhanced expressive power achieved by these classes of process algebras has allowed to ... |

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105 |
Stochastic π-calculus
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Citation Context ...ocess algebras (see e.g. [47, 30, 58, 37, 34, 5, 56]), deterministically timed process algebras (see e.g. [52, 3, 41, 51, 39, 20, 60, 23, 36, 19]), and stochastically timed process algebras (see e.g. =-=[42, 24, 27, 12, 2, 21, 53, 26, 11, 45, 25, 31, 46]-=-). The enhanced expressive power achieved by these classes of process algebras has allowed to model and analyze a greater number of characteristics with respect to classical process algebras such as i... |

97 |
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95 | An implementation of an efficient algorithm for bisimulation equivalence
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- 1990
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Citation Context ...e actions are concerned. In Section 5.5 we give a sound and complete axiomatization of ��EMB for the set of nonrecursive terms of EMPA. Finally, in Section 5.6 we develop an algorithm in the style=-= of [16] that ca-=-n be used both to check two EMPA terms for ��EMB and to minimize the integrated semantic model of an EMPA term, and we show the relationship between ��EMB and ordinary lumping. Proofs of resul... |

81 |
On the Advantage of Free Choice: A Symmetric and Fully Distributed Solution to the Dining Philosophers Problem
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- 1981
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Citation Context ...?:!eat i ; ?:!pd i ; ?:!pd i+n 1 ; ?:P i UBLCS-96-17 18 5 A notion of equivalence for EMPA To solve the problem in a more elegant and fair manner, we could use the randomized distributed algorithm of =-=[24]-=-: P i flips a fair coin to choose between C i and C i+1 , gets the chosen chopstick as soon as it becomes free, and gets the other chopstick if it is free, otherwise releases the chosen chopstick and ... |

76 |
Syntax and defining equations for an interrupt mechanism in process algebra
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Citation Context ...lassical process algebras was enriched by allowing for the modeling of real-world features such as priorities, probabilities and durations, thereby resulting in prioritized process algebras (see e.g. =-=[4, 14, 13, 57, 17, 15]-=-), probabilistic process algebras (see e.g. [47, 30, 58, 37, 34, 5, 56]), deterministically timed process algebras (see e.g. [52, 3, 41, 51, 39, 20, 60, 23, 36, 19]), and stochastically timed process ... |

73 |
Equivalences, congruences, and complete axiomatizations for probabilistic processes
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Citation Context ...modeling of real-world features such as priorities, probabilities and durations, thereby resulting in prioritized process algebras (see e.g. [2, 11, 12, 39]), probabilistic process algebras (see e.g. =-=[21, 40, 14, 25, 3, 36]-=-), deterministically timed process algebras (see [28, 15] and the references therein), and stochastically timed process algebras (see [31, 32, 33, 34] and the references therein). The enhanced express... |

70 |
CCS + Time = an Interleaving Model for Real Time Systems
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68 |
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Citation Context ... of real-world features such as priorities, probabilities and durations, thereby resulting in prioritized process algebras (see e.g. [4, 14, 13, 57, 17, 15]), probabilistic process algebras (see e.g. =-=[47, 30, 58, 37, 34, 5, 56]-=-), deterministically timed process algebras (see e.g. [52, 3, 41, 51, 39, 20, 60, 23, 36, 19]), and stochastically timed process algebras (see e.g. [42, 24, 27, 12, 2, 21, 53, 26, 11, 45, 25, 31, 46])... |

51 |
Processes with Probabilities, Priority and Time
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Citation Context ...modeling of real-world features such as priorities, probabilities and durations, thereby resulting in prioritized process algebras (see e.g. [2, 11, 12, 39]), probabilistic process algebras (see e.g. =-=[21, 40, 14, 25, 3, 36]-=-), deterministically timed process algebras (see [28, 15] and the references therein), and stochastically timed process algebras (see [31, 32, 33, 34] and the references therein). The enhanced express... |

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Citation Context ...ocess algebras (see e.g. [47, 30, 58, 37, 34, 5, 56]), deterministically timed process algebras (see e.g. [52, 3, 41, 51, 39, 20, 60, 23, 36, 19]), and stochastically timed process algebras (see e.g. =-=[42, 24, 27, 12, 2, 21, 53, 26, 11, 45, 25, 31, 46]-=-). The enhanced expressive power achieved by these classes of process algebras has allowed to model and analyze a greater number of characteristics with respect to classical process algebras such as i... |

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Citation Context ...ion 6 we report some concluding remarks on further enhancements of the expressiveness of EMPA and the related consequences on the complexity of the underlying theory. This tutorial is based mainly on =-=[9, 7]-=- and constitutes a revised version of both of them. With respect to [9], we emphasize the coexistence of several kernels and the resulting expressive power like in [7]; unlike [7], passive actions are... |

44 | The Nature of Synchronisation
- Hillston
- 1994
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Citation Context ...rthermore, possible subsequent changes of the rate affect only one component. As observed in Section 3, to compute correctly the rate of a synchronization according to the bounded capacity assumption =-=[28]-=-, which states that the rate at which a term carries out an action cannot be increased in case of synchronization, a normalization is required that takes into account the number of alternative or inde... |

42 |
CCS with priority choice
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Citation Context ...lassical process algebras was enriched by allowing for the modeling of real-world features such as priorities, probabilities and durations, thereby resulting in prioritized process algebras (see e.g. =-=[4, 14, 13, 57, 17, 15]-=-), probabilistic process algebras (see e.g. [47, 30, 58, 37, 34, 5, 56]), deterministically timed process algebras (see e.g. [52, 3, 41, 51, 39, 20, 60, 23, 36, 19]), and stochastically timed process ... |

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Citation Context ...modeling of real-world features such as priorities, probabilities and durations, thereby resulting in prioritized process algebras (see e.g. [2, 11, 12, 39]), probabilistic process algebras (see e.g. =-=[21, 40, 14, 25, 3, 36]-=-), deterministically timed process algebras (see [28, 15] and the references therein), and stochastically timed process algebras (see [31, 32, 33, 34] and the references therein). The enhanced express... |

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Citation Context ...d O(m + n) space where n is the number of states and m is the number of transitions. It is worth noting that a variant of the algorithm in Table 7 can be used to compute the coarsest ordinary lumping =-=[37]-=- of the Markovian semantics of a given term, hence allowing for the determination of performance measures by solving a smaller Markov chain which is equivalent to the original one. Definition 5.34 Let... |

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